Hierarchical Plasmon Resonances in Fractal Structures

Abstract

An equilateral triangular prism is used as the fundamental building block to construct additive Sierpiński fractals, enabling new surface plasmon resonances (SPR) in the first three generations of Sierpiński triangles, as well as topological intermediaries between generations. The modes are characterized using electron energy loss spectroscopy accompanied by eigenmode calculations and optical finite-difference time-domain simulations. The complex fractal geometries present a predictable hierarchy of new resonances, each arising from the previous generational building blocks used to construct the fractal. Intermediate structures break the polarization degeneracy of the equilateral fractals while maintaining a rich multiband spectral response. Engineering defects in the narrow conductive channels of the fractal allows further manipulation of the SPR response, emphasizing higher order SPR modes over the lowest energy peak. The knowledge gained is used to develop guidelines for engineering the response of more complex fractal-based structures, including the spectral response and hotspot distribution.